Common use of Semantics Clause in Contracts

Semantics. This section discusses the semantics of the flow language and the way to integrate it with Event-B. In particular we show how to reason about flow and machine consistency in the terms of machine properties rather than flow or machine traces. But first we use the traces semantics to formally integrate flows with Event-B. The following defines the traces of a flow expression. traces(jskip) = {()} ^j j ntraces( stop) = s n s stop traces(jstart) = {(jstart)} { | ∈ N ∧ ≤ ( ) } =^^ ^ ^ js z s z traces(p) z = stop traces(ei.a) traces(p; q) traces(p|q) traces(∗(p)) = {(ei.a)} {s^t | s^z ∈ traces(p) ∧ t ∈ traces(q) ∧ z ƒ= (jstop)} =^ traces(p (p; (p))) = traces(p) ∪ traces(q) ^ S ^ | ∗ traces(p E q) = (s Et s traces(p) t traces(q) Here s t states that trace s is a prefix of trace t; α(x) is an alphabet of x (set of all events occurring in x). The parallel composition operator is defined as a collection of possible event interleavings:

Semantics. This section discusses the semantics of the flow language and the way to integrate it with Event-B. In particular we show how to reason about flow and machine consistency in the terms of machine properties rather than flow or machine traces. But first we use the traces semantics to formally integrate flows with Event-B. The following defines the traces of a flow expression. traces(jskip) = {()} ^j bj j ntraces( stop) = s n s stop traces(jstart) = {(jstart)} { traces( stop) = {s | n ∈ N ∧ s ≤ ( stop) } =^^ ^ ^ js z s z traces(p) z = stop b {( )} traces(ei.a) traces(p; q) traces(p|q) traces(∗(p)) traces(pǁEq) = ei.a b {(ei.a)} s z | s z ∈ traces(p) ∧ z = ( stop)}∪ = ^ ^ j {s^t | s^z ∈ traces(p) ∧ t ∈ traces(q) ∧ z ƒ= =ƒ (jstop)} =^ b = traces(p) ∪ traces(q) b | ∗ = traces(p (p; (p))) = =b {S(sǁEt | s ∈ traces(p) ∪ ∧ t ∈ traces(q) ^ S ^ | ∗ traces(p E q) = (s Et s traces(p) t traces(q) )} Here s t states that trace s is a prefix of trace t; α(x) is an alphabet of x (set of all events occurring in x). The parallel composition operator is defined as a collection of possible event interleavings: